Question

A body of mass m hung at one end of the spring executes SHM. where K is the force
constant of the spring. prove that the relation given below is incorrect, also
derive correct relation.
T= 2πm/K​

Answer 1

Answer:

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Explanation:

Answer :

Cmk−−−√

Solution :

The given equation is T=2πmk

Taking the dimensions of both sides, we have

[T]=[M][ML0T−2]=T2

As the dimensions of two sides are not equal , hence the equation is incorrect.

Let the correct relation be T=Cmakb,whereC is constant. Equating the dimensions of both sides , we get

[T]=[M]a[MT−2]b

or [M0L0T]=[Ma+bL0T−2b]

Comparing the powers of M,L, and T on both sides , we get a+b=0and−2b=1.

Therefore , b=−12anda=12

:. T=Cm−1/2k−1/2=Cmk−−−√

This is the correct equation.

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Answer 2

Answer:

A body of mass m hung at one end of the spring executes simple harmonic motion . The force constant of a spring is k while its period of vibration is T. Prove by dimensional method that the equation T=2πm/k is correct. ... As the dimensions of two sides are not equal , hence the equation is incorrect

Explanation:

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